PC cgDNA+min: Kahn & Crothers sequence

Periodic closure cgDNA+min results for the 4 initial guesses highlighted in the following bifurcation diagram:

Solutions A and D represent the same configuration as well as solutions B and C. We see that initial guess B outputs a solution that is not a proper minimizer. Since the norm of the negative eigenvalue is very small and since we see that solution C, which represents the same configuration, has a positive definite Hessian, we can conclude that the negative eigen value is comming from the fact that the configuration shown in B is not exacly the minimum but a configuration very close. The algorithm stopped before getting to the minimum because of the size of the step size becoming too small.

Solution for initial guess A:

Link Energy Smallest Eigenvalue
Initial guess A 15 4012 -
Solution A 15 47 5.12e-6





MATLAB figures saved variables:
Kahn-Crothers_3Dsol1_PCcgDNA+min.fig
Kahn-Crothers_2Dsol1_PCcgDNA+min_cgDNA-coord.fig
Kahn-Crothers_2Dsol1_PCcgDNA+min_Pho-coord.fig
Kahn-Crothers_sol1_PCcgDNA+min.mat

Solution for initial guess B:

Link Energy Smallest Eigenvalue
Initial guess B 14 4970 -
Solution B 16 118 -4.30e-6





MATLAB figures and saved variables:
Kahn-Crothers_3Dsol2_PCcgDNA+min.fig
Kahn-Crothers_2Dsol2_PCcgDNA+min_cgDNA-coord.fig
Kahn-Crothers_2Dsol2_PCcgDNA+min_Pho-coord.fig
Kahn-Crothers_sol2_PCcgDNA+min.mat

Solution for initial guess C:

Link Energy Smallest Eigenvalue
Initial guess C 14 5048 -
Solution C 16 117 1.11e-5





MATLAB figures and saved variables:
Kahn-Crothers_3Dsol4_PCcgDNA+min.fig
Kahn-Crothers_2Dsol4_PCcgDNA+min_cgDNA-coord.fig
Kahn-Crothers_2Dsol4_PCcgDNA+min_Pho-coord.fig
Kahn-Crothers_sol4_PCcgDNA+min.mat

Solution for initial guess D:

Link Energy Smallest Eigenvalue
Initial guess D 15 7111 -
Solution D 15 47 5.86e-6





MATLAB figures and saved variables:
Kahn-Crothers_3Dsol10_PCcgDNA+min.fig
Kahn-Crothers_2Dsol10_PCcgDNA+min_cgDNA-coord.fig
Kahn-Crothers_2Dsol10_PCcgDNA+min_Pho-coord.fig
Kahn-Crothers_sol10_PCcgDNA+min.mat